Encoding data into constrained memory using a method for writing data that includes receiving write data to be encoded into a write word, receiving constraints on symbol values associated with the write word, encoding the write data into the write word, and writing the write word to a memory. The encoding includes: representing the write data and the constraints as a first linear system in a first field of a first size; embedding the first linear system into a second linear system in a second field of a second size, the second size larger than the first size; solving the second linear system in the second field resulting in a solution; and collapsing the solution into the first field resulting in the write word, the write word satisfying the constraints on symbol values associated with the write word.